Wales fought out a goalless draw to give them a fighting chance of winning their way through to the championships in Portugal in Wednesday's second leg.
But the flashpoint came after a crude lunge by Vadim Evseev in the second half, which Hughes was furious went unpunished.
In the aftermath, the Russia full back went down clutching his face after Giggs had returned to the pitch after treatment and the pair had clashed.
Hughes told the BBC: "The tackle was terrible, it was something you do not want to see. I was amazed it went unpunished.
"And the way their lad went down soon after, it did look like they were trying to get Ryan sent off.
"It was theatrical. Quite possibly they were at a stage when they needed to make something happen for them and maybe the felt by us losing a player it would help them.
"Ryan showed great restraint. But they are experienced international players now and they play a lot of club football in Europe, they know what happens and that experience came to the forefront."
Hughes was also worried by the flares which rained down onto the pitch and caused two stoppages in play.
"You do not want to see that either. We were all a little worried about the flares, we did not expect they would reach the playing surface," added the Wales boss.
"It bothered me that because of the hold-ups there would be more time added on at the end."
Wales emerged from a searching examination with a confidence-boosting draw ahead of Wednesday's second leg at the Millennium Stadium.
Hughes said: "We all knew we had to produce a peak performance. You only get so many chances at this level, we should have qualified outright but now we have another opportunity and we intend to take it.
"We must get very careful we do not get ahead of ourselves now. That is what happened in the qualifying games when we did not beat Serbia and Finland when we expected to.
"That experience has helped us now. Afterwards the lads were delighted with the level of performance, but everyone knows it is only half way. We have had false dawns before but we do not want anymore glorious failures."
Hughes hailed his unsung heroes in Danny Gabbidon, Jason Koumas and Darren Barnard who came in to produced outstanding displays.
He said: "Every time Danny steps up to international football excels. He is a young man making a big name for himself.
"Jason was super on the night. He gave us something extra on the right and it was an area we could exploit. He could run, carry possession and was outstanding for us, as was Darren Barnard.
"He has had two excellent back-to-back performances for us and I could not have asked for anything more."
Russian counterpart Georgy Yartsev said Wales would probably start the second leg as favourites, given their home advantage.
"The final score is, surely, more preferable for our opponents as they'll play at home. I'm disappointed with the result though I'm pleased with the performance of my players. We're surprised with the opponents' discipline and good performance in defence. Our main success today is that we have neutralized Giggs," he said.
"I don't want to comment the episode when Giggs pushed Evseev with his elbow: Let Uefa watch the video and decide.
"We're seriously disappointed with the fact that Ovchinnikov and Mostovoy will miss the game in Cardiff. I can't understand our goalie, who got his yellow card not in the game but after the first half for what he said to the referee.
"Kerzhakov didn't take part in the game because we thought that trio Mostovoy-Alenichev-Sychev will be more useful. As for the game in Cardiff, I can say that our reserve-goalies - Malafeev and Akinfeev - have equal chances to start in the first eleven.
"Egor Titov, who missed today's game because of an injury, will also most likely play in that game. We're not planning only to defend in Cardiff but we also won't play in a very attacking style."
Viktor Onopko, Russian team captain added: ‚Ç£Our opponents didn't score and we had good chances to score, though it's a pity we didn't. We'll do our best in Cardiff.
"We're not frightened with the capacity of ‚Ç£Millennium‚Ç¥ stadium. We have lots of experienced players who won't be shaken with that support. We'll fight until the end.‚Ç¥
